Fast Approximate Inverse Bayesian Inference in non-parametric Multivariate Regression
with application to palaeoclimate reconstruction
A thesis submitted to the University of Dublin, Trinity College
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
Department of Statistics, School of Computer Science and Statistics
University of Dublin, Trinity College

PIC

April 2009
Michael Salter-Townshend

 Declaration
Abstract
Acknowledgements
Contents
List of Tables
List of Figures
 Publications
1 Introduction
 1.1 Palaeoclimate Reconstruction Project
 1.2 Computational Challenges
 1.3 Overview of Chapters
 1.4 Research Contributions
2 Literature Review and Statistical Methodology
 2.1 Palaeoclimate Reconstruction Literature Review
 2.2 Relevant Bayesian Methods
 2.3 Integrated Nested Laplace Approximations
 2.4 Spatial Zero-Inflated Models
 2.5 Inverse Regression
 2.6 Model Validation
 2.7 Conclusions
3 Models with Known Parameters
 3.1 The Univariate Problem
 3.2 Disjoint-Decomposable Models
 3.3 Multivariate Normal Model
 3.4 Counts Data
 3.5 Compositional Data
 3.6 Conclusions
4 INLA Inference and Cross-Validation
 4.1 The Integrated Nested Laplace Approximation
 4.2 Cross Validation
 4.3 Conclusions
5 Inference Methodology
 5.1 Reasons for Disjoint-Decomposition
 5.2 Multivariate Normal Model
 5.3 Sensitivity to Inference via Marginals
 5.4 Conclusions
6 Application: the Palaeoclimate Reconstruction Project
 6.1 Bayesian Palaeoclimate Reconstruction Project
 6.2 Model Description
 6.3 Zero-Inflation
 6.4 Results
 6.5 Conclusions
7 Conclusions and Further Work
 7.1 Conclusions
 7.2 Further Work
Bibliography

Declaration

This thesis has not been submitted as an exercise for a degree at any other University. Except where otherwise stated, the work described herein has been carried out by the author alone. This thesis may be borrowed or copied upon request with the permission of the Librarian, University of Dublin, Trinity College. The copyright belongs jointly to the University of Dublin and Michael Salter-Townshend.

------------------------------------------ Michael Salter-Townshend Dated: July 17, 2009